Tau neutrino deep inelastic charged current interactions

The ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation hypothesis will be tested through ${\nu }_{\tau }$ production of $\tau$ in underground neutrino telescopes as well as long-baseline experiments. We provide the full QCD framework for the evaluation of tau neutrino deep inelastic charged current (CC) cross sections at leading twist, including next-to-leading-order (NLO) corrections, charm production, tau threshold, and target mass effects in the collinear approximation. We investigate the violation of the Albright-Jarlskog relations for the structure functions $F_{4,5}$ which occur only in heavy lepton $\left(\tau \right)$ scattering. Integrated CC cross sections for neutrino-nucleon interactions are evaluated naively over the full phase space and with the inclusion of DIS kinematic cuts. Uncertainties in our evaluation based on scale dependence, PDF errors and the interplay between kinematic and dynamical power corrections are discussed and/or quantified.